Speedy Printing charges $23 for 200 deluxe business cards and $35 for 500 deluxe business cards. Given that the cost is a linear function of the number of cards printed, find a formula for that function and find the cost of 700 business cards.
It would help if you proofread your questions before you posted them.
Since they are both "deluxe business cards," I would only get the ones at the lower rate.
23/x = 200/700
Solve for x.
But that formula does not account for the 39% discount given on the 500 cards.
To find the formula for the cost of printing deluxe business cards, we need to determine the rate at which the cost changes with the number of cards printed. We can do this by finding the slope of the line that represents the cost.
Let's call the number of cards printed "x" and the cost "y". We are given two points on the line: (200, 23) and (500, 35).
Using the formula for the slope:
slope = (y2 - y1)/(x2 - x1)
slope = (35 - 23)/(500 - 200)
slope = 12/300
simplify the slope: slope = 0.04
Next, we need to find the y-intercept of the line. We can do this by substituting the values of one of the points into the equation y = mx + b, where m is the slope and b is the y-intercept.
Using the point (200, 23):
23 = 0.04 * 200 + b
23 = 8 + b
b = 23 - 8
b = 15
Now we have the slope, which is 0.04, and the y-intercept, which is 15. We can write the equation for the cost of printing deluxe business cards:
y = 0.04x + 15
To find the cost of printing 700 business cards, we substitute x = 700 into the equation:
y = 0.04 * 700 + 15
y = 28 + 15
y = 43
Therefore, the cost of printing 700 business cards is $43.